This thesis focuses on one area of modern condensed matter physics,
namely low-dimensional magnetism, and more specifically one-dimensional
linear chains. The work herein can be split into three parts. The
first part provides a tool for the greater community. I herein propose a
Pad´e approximation for the temperature dependent magnetic susceptibility
of a S = 3/2 spin chain, that is more accurate than those already
known. The approximation allows one to fit experimentally measured
magnetic susceptibilities and ascertain values such as the near-neighbour
spin exchange interaction and the g-factor. The second and third parts
of this thesis are both concerned with experimentally and theoretically
characterizing two isostructural linear S = 1/2 chain compounds on opposite
ends of the 3d transition metal series. The compounds, CuCrO4
(3d9) and TiPO4 (3d1), are shown to have completely different ground
states despite both being largely isostructural and S = 1/2 quantum
spin systems. In this work and the resulting publications it is shown that
CuCrO4 is a one-dimensional S = 1/2 spin chain with anti-ferromagnetic
nearest- and next nearest-neighbour spin exchange interactions. The
ratio of these spin exchange interactions is shown experimentally and
theoretically to be approximately 2, putting CuCrO4 in the vicinity of
the Majumdar-Ghosh point, for which the magnetic ground-state can
ii
be solved analytically. Small ferromagnetic inter-chain coupling leads
to long-range ferromagnetic ordering between anti-ferromagnetic chains
at 8.2(2) K. At this temperature a spontaneous electrical polarization
is observed. This classifies CuCrO4 as a type-II multiferroic. Contrary
to CuCrO4, TiPO4 has a non-magnetic ground state. At 111 and 74 K
TiPO4 undergoes a two stage phase transition, which is interpreted as
a spin-Peierls transition. There is evidence that below 74 K TiPO4 has
a new crystal structure, in which there are alternating dimerised chains
and two different PO4 tetrahedral units. Currently the new structure
has not been identified and no super-structure reflections have been confirmed
in either low-temperature neutron or x-ray diffraction.
In summary this thesis presents some experimental and theoretical contributions
to the field of low-dimensional magnetism.

Description:

A Doctoral Thesis. Submitted in partial fulfillment of the requirements for the award of Doctor of Philosophy of Loughborough University.